# Chordal Decomposition for Spectral Coarsening

arXiv: https://arxiv.org/abs/2009.02294 · HTML: https://mlsanity.com/paper/2009.02294/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2020.

## Built on by (most cited first, 2 of 2)

- [Chordal Sparsity for Lipschitz Constant Estimation of Deep Neural Networks](https://mlsanity.com/paper/2204.00846/) (2022)
- [Chordal Sparsity for SDP-based Neural Network Verification](https://mlsanity.com/paper/2206.03482/) (2022)

## Abstract (arXiv)

We introduce a novel solver to significantly reduce the size of a geometric operator while preserving its spectral properties at the lowest frequencies. We use chordal decomposition to formulate a convex optimization problem which allows the user to control the operator sparsity pattern. This allows for a trade-off between the spectral accuracy of the operator and the cost of its application. We efficiently minimize the energy with a change of variables and achieve state-of-the-art results on spectral coarsening. Our solver further enables novel applications including volume-to-surface approximation and detaching the operator from the mesh, i.e., one can produce a mesh tailormade for visualization and optimize an operator separately for computation.